Fourier terms for modelling seasonality

fourier returns a matrix containing terms from a Fourier series, up
to order K, suitable for use in Arima,
auto.arima, or tslm.

fourier(x, K, h=NULL)
fourierf(x, K, h)

Arguments

x

Seasonal time series: a ts or a msts object

K

Maximum order(s) of Fourier terms

h

Number of periods ahead to forecast (optional)

Value

Numerical matrix.

Details

fourierf is deprecated, instead use the h argument in
fourier.

The period of the Fourier terms is determined from the time series
characteristics of x. When h is missing, the length of
x also determines the number of rows for the matrix returned by
fourier. Otherwise, the value of h determines the number of
rows for the matrix returned by fourier, typically used for
forecasting. The values within x are not used.

Typical use would omit h when generating Fourier terms for training a model
and include h when generating Fourier terms for forecasting.

When x is a ts object, the value of K should be an
integer and specifies the number of sine and cosine terms to return. Thus,
the matrix returned has 2*K columns.

When x is a msts object, then K should be a vector of
integers specifying the number of sine and cosine terms for each of the
seasonal periods. Then the matrix returned will have 2*sum(K)
columns.